Reinvestigating the R2 Indicator: Achieving Pareto Compliance by Integration

Research output: Contribution to book/Conference proceedings/Anthology/ReportConference contributionContributedpeer-review

Abstract

In multi-objective optimization, set-based quality indicators are a cornerstone of benchmarking and performance assessment. They capture the quality of a set of trade-off solutions by reducing it to a scalar number. One of the most commonly used set-based metrics is the R2 indicator, which describes the expected utility of a solution set to a decision-maker under a distribution of utility functions. Typically, this indicator is applied by discretizing this distribution of utility functions, yielding a weakly Pareto-compliant indicator. In consequence, adding a nondominated or dominating solution to a solution set may – but does not have to – improve the indicator’s value. In this paper, we reinvestigate the R2 indicator under the premise that we have a continuous, uniform distribution of (Tchebycheff) utility functions. We analyze its properties in detail, demonstrating that this continuous variant is indeed Pareto-compliant – that is, any beneficial solution will improve the metric’s value. Additionally, we provide an efficient computational procedure to compute this metric for bi-objective problems in O(NlogN). As a result, this work contributes to the state-of-the-art Pareto-compliant unary performance metrics, such as the hypervolume indicator, offering an efficient and promising alternative.

Details

Original languageEnglish
Title of host publicationParallel Problem Solving from Nature – PPSN XVIII
EditorsMichael Affenzeller, Stephan M. Winkler, Anna V. Kononova, Thomas Bäck, Heike Trautmann, Tea Tušar, Penousal Machado
Pages202-216
Number of pages15
ISBN (electronic)978-3-031-70085-9
Publication statusPublished - 7 Sept 2024
Peer-reviewedYes

Publication series

SeriesLecture Notes in Computer Science
Volume15151
ISSN0302-9743

External IDs

Scopus 85204641244
ORCID /0000-0003-3929-7465/work/168718802
ORCID /0000-0003-2862-1418/work/168719590

Keywords

Keywords

  • Benchmarking, Multi-objective optimization, Pareto compliance, Performance assessment, R2 indicator, Utility functions